Just quicky try without any precision (just for the concept) but maybe that could be work :)

With more attention to the orientation and size of circles )
In fact that is not a verygood idea :D

Just a little question : When an arc is "extended" to a boundary object : it's an always an arc or a certain tangent line from the existant arc toward the boundary object?

Ps Very sinuous grooves Michael and tricky tip ! :)